In a bowl, mix the sliced beef, egg white, cornstarch, salt, and black pepper until well coated.
Let it sit for about 10 minutes while you prepare the sauce and vegetables.
In a small bowl, whisk together hoisin sauce, soy sauce, vinegar, sugar, ketchup, and red pepper flakes.
In a separate small dish, mix 1 teaspoon cornstarch with 2 tablespoons water to create a slurry for thickening.
Heat about ½ inch of oil in a pan over medium-high heat.
Once hot, fry the beef in batches, cooking for 2-3 minutes per side until crispy.
Remove and drain on a plate lined with paper towels.
In a wok or large pan, heat 1 tablespoon oil over medium heat.
Add garlic, ginger, onions, and bell peppers, stir-frying for 2-3 minutes until slightly softened.
Pour the prepared sauce into the pan with the vegetables.
Stir in the cornstarch slurry and cook for 1-2 minutes until thickened.
Add the fried beef and toss everything together until well coated.
Remove from heat and serve immediately over steamed rice or noodles.
Enjoy your homemade Beijing Beef!